A060061 Fourth column of triangle A060058.

61, 1385, 12284, 68060, 281210, 948002, 2749340, 7097948, 16700255, 36419955, 74551048, 144631240, 267951892, 476948260, 819683560, 1365672424, 2213323585, 3499318141, 5410278500, 8197124100

Offset

0,1

Comments

a(n)= sum(j3^2*sum(j2^2*sum(j1^2,j1=1..j2+1),j2=1..j3+1),j3=1..n), threefold iterated sums of squares).

Links

Indranil Ghosh, Table of n, a(n) for n = 0..5000

Formula

a(n)=A060058(n+3, 3) = binomial(n+6, 6)*(280*n^3+2436*n^2+5906*n+3843)/(7*9).

G.f. (61+775*x+1179*x^2+225*x^3)/(1-x)^10 = p(3, x)/(1-x)^(3*3+1) with p(3, x)=sum(A060063(3, m)*x^m, m=0..3).

Mathematica

Table[Binomial[n+6, 6]*(280*n^3+2436*n^2+5906n+3843)/63, {n, 0, 19}] (* Indranil Ghosh, Feb 21 2017 *)

Prog

(Python)
import math
def C(n, r):
....f=math.factorial
....return f(n)/f(r)/f(n-r)
def A060061(n):
....return (C(n+6, 6)*(280*n**3+2436*n**2+5906*n+3843))/63 # Indranil Ghosh, Feb 21 2017

Crossrefs

Cf. A000330, A060060.

Sequence in context: A218112 A154428 A262017 * A000507 A350974 A143011

Adjacent sequences: A060058 A060059 A060060 * A060062 A060063 A060064

Keyword

nonn,easy

Author

Wolfdieter Lang, Mar 16 2001

Status

approved